ae6450 fall 2008 lecture #5 nozzles

EXTROVERT Space Propulsion 05

AE6450 Fall 2008Lecture #5

Nozzles

• Types of nozzles• Expansion Ratio criteria• Nozzle heat transfer and materials issues

In this lecture we will cover:

EXTROVERT Space Propulsion 05NOZZLES

The function of the rocket nozzle is to convert the thermal energy in the propellant into kinetic energy as efficiently as possible, in order to obtain high exhaust velocity along the desired direction.

The mass of a rocket nozzle is a large part of the engine mass. Many of the failures encountered in rocket engines are also traceable to failures of the nozzle – historical data suggest that 50% of solid rocket failures stemmed from nozzle problems.

The design of the nozzle must trade off:

1. Nozzle size (needed to get better performance) against nozzle weight penalty. 2. Complexity of the shape for shock-free performance vs. cost of fabrication


T-s Diagram (or h-s Diagram) for a nozzle: Ideal

i: reactants at chamber pressure p0

f: final mixture at combustion chamber stagnation conditions p0 ,T0t: throat conditions. Mach 1, p*, T*

e: exit conditions pe ,Te (assuming fully expanded)

i

f

t

e

T

Entropy s

p0

pe

p*

T0Q/cp

EXTROVERT Space Propulsion 05T-s Diagram (or h-s Diagram) for a nozzle: with losses

i: reactants at chamber pressure p0i

f: final mixture at combustion chamber stagnation conditions p0 ,T0 t: throat conditions. Mach 1, p*, T*

e: exit conditions pe ,Te (assuming fully expanded).

i

f

t

e

T

Entropy s

p0

pe

p*

T0Q/cp

Losses show up as increases in entropy for each step – usually accompaniedby a loss of pressure. At the exhaust, note that exhaust temperature is higherthan ideal when the final pressure is reached.


Recall – Expressions for Thrust Coefficient - 1

where At is nozzle throat area and p0 is chamber pressure (N/m2)

Thus,

For sonic conditions at the throat,

and


Using isentropic flow relations,

and Thrust Coefficient

Depends entirely on nozzle characteristics. The thrust coefficient is used to evaluate nozzle performance.

Thrust Coefficient - 2


Used to characterize the performance of propellants and combustion chambers independent of the nozzle characteristics.

where is the quantity in brackets. Note:

So

Characteristic velocity

Assuming steady, quasi-1-dimensional, perfect gas. The condition for maximum thrust is ideal expansion: nozzle exit static pressure being equal to the outside pressure. In other words,

Characteristic Velocity c*

EXTROVERT Space Propulsion 05Nozzle Types

The subsonic portion of the nozzle is quite insensitive to shape – the subsonic portion of the acceleration remains isentropic. The divergent nozzle is where the decisions come into play.

Conical Nozzle• Easier to manufacture – for small thrusters• Divergence losses: Exit velocity is not all in the desired direction.

Bell Nozzle• Complex shape• Highest efficiency (near axial flow at exhaust)• Large base drag during atmospheric flight after burnout

Plug Nozzle or Aerospike Nozzle (linear or annular) (X-33, VentureStar, 1960s concept )• Altitude compensating (see Chang 3-30c)

Expansion- Deflection Nozzle (E-D)• Shortest nozzle of the “enclosed” types.

EXTROVERT Space Propulsion 05Conical Nozzle

0**

'c RT

Cη γ

=Γ

· Easier to manufacture – for small thrusters

· Divergence losses: Exit velocity is not all in the desired direction.

a

Here l is the “thrust efficiency”, defined as ratio of actual to ideal thrust , accounting for flow divergence.

e is the nozzle Area Ratio (ratio of exit area to throat area).

Note: a can be as large as 12 to 18 degrees.

EXTROVERT Space Propulsion 05Geometric Representations of Nozzles

:

ax

y

R1

N2Rt

RtThroat internal radius

N Transition point from circular contour to conical contour. Located along at angle a downstream of throat.

LN

ReExit radius

Radius of curvature of the nozzle contractionR1

Cone nozzle

Nozzle Length: LN

For a conical nozzle, is a typical choice.

EXTROVERT Space Propulsion 05Bell Nozzle

• Complex shape• Highest efficiency (near axial flow at exhaust)• Large Base Drag during atmospheric flight after burnoutA true bell nozzle is contoured to minimize the turning (compression) shock losses at the wall as the flow expands, but still turning the flow towards an axial exhaust. Note that the flow may still be under-, over- or fully-expanded at the exit, and hence shocks / expansions may exist downstream.

EXTROVERT Space Propulsion 05Bell Nozzle

An approximate shape can be formed from a parabola (after G.V.R. Rao)

q1

x

y’

R1

NRt

L

x’

Upstream of the throat

qe

Downstream of the throat

EXTROVERT Space Propulsion 05Parabolic Bell Nozzle Contour, cont’d (Rao, 1958)

There are 4 unknowns in the rotated parabolic segment equation (P,Q,S,T) and 4 boundary conditions

1. At N:

2. At e:

Or,

3. At N: is given (Rao, 1958, plots)

2. At e: is given (Rao, 1958, plots)

(see Humble p. 225)

EXTROVERT Space Propulsion 05So, 1. and hence …………………..(A) 2. and ……………… (B) 3.

………………………….. (C)

(from (A))

4.

…………… (D)


Equating (B) = (D) leads after some manipulation, to

…………… (E)

Also, squaring (B)

…………… (F)

Substituting for Q from (C),

Eventually gives

Down to one unknown.

…… (G)


Use eqn. (G) to find

Then either (F) or (E) to get S

Then use (C) to get QThen use (A) to get T in terms of the original X,Y axes.

Recall:

and

where L is generally a fraction of that for a 15-degree half-angle cone

with the same R1 (i.e., 0.382Rt)

f = 100%; 90% or 80% of a 15-degree cone.


Comparison of bell and cone nozzles

For the same e, we would expect

A bell nozzle, while more complex to build, will generally yield a more efficient exhaust than a cone in a shorter nozzle length.

Same nozzle efficiency factor can be reached with about 70% of the length of a cone nozzle.

Alternatively, efficiency factor can be increased from about 98% for a cone to about 99.2% for a bell of the same length


Types of Nozzles

• Types of nozzles• Expansion Ratio criteria• Nozzle heat transfer and materials issues

In this lecture we will continue the discussion on nozzles:


E-D: Expansion-DeflectionSpike: “Plug”R-F: Reverse FlowH-F: Horizontal Flow

http://www.aerospaceweb.org/design/aerospike/shapes.shtml

Comparison of Optimal Nozzles (source: Huzel & Huang, 1967)


Annular Nozzles

Expansion-Deflection Nozzle and Plug Nozzle

• Substantially shorter than conical or bell nozzles for the same thrust and area ratio. • Design-point performance is nearly as good. • Off-design performance is better under conditions where conventional nozzles

would be over-expanded.

• Common feature: Free shear layer bounding nozzle flow.

EXTROVERT Space Propulsion 05Spike Nozzle Flow Geometries

http://www.aerospaceweb.org/design/aerospike/inflow.shtml

[from Berman and Crimp, 1961]

External expansion Internal-external expansion

Internal expansion




[from Berman and Crimp, 1961]Effect of Replacing Spike with Cone



EXTROVERT Space Propulsion 05Aerospike

Truncates full spike and adds secondary base flow to help contour the inner flow.

Source: Hill & Peterson, p. 540

http://www.aerospaceweb.org/design/aerospike/aerospike.shtml

EXTROVERT Space Propulsion 05Aerospike Flow Features

RocketdyneRS2200. Flynn, 1996

Ruf and McConnaughey, 1997

Thrust = Fthruster+Fcenterbody+Fbase

http://www.aerospaceweb.org/design/aerospike/aerodynamics.shtml

EXTROVERT Space Propulsion 05Theoretical Performance Comparison

[from Huzel and Huang, 1967]

http://www.aerospaceweb.org/design/aerospike/compensation.shtml

Note: The aerospike is susbtantially better at low altitudes where the belland cone are likely to be overexpanded.


Linear Aerospike

Combustion chamber modules placed along the inside.

EXTROVERT Space Propulsion 05Advantages and Disadvantages

Advantages• Much smaller size• Altitude compensation• Lower chamber pressure / higher expansion ratio: safer• Lower vehicle drag• Lower vehicle weight• Modular: lower manufacture and repair costs; lower downtime• Thrust Vectoring: mass flow through individual elements can be controlled.

Disadvantages• Heating.• More complex geometry• ??? (not much experience to-date)

Rocketdyne, ’99

http://www.aerospaceweb.org/design/aerospike/x33.shtml

EXTROVERT Space Propulsion 05Combustor Geometry

Spherical (usually for

solid rockets Cylindrical Chamber

Ac At

Lc

q

= contraction ratioFor a cylindrical chamber

Chamber Volume

Convergent part approximated as conical

EXTROVERT Space Propulsion 05Scaling relation between the combustion-chamber length and

Contraction Ratio

Assuming we get theta from the throat geometry, how do we find ?Characteristic Length L*

L* is empirically determined for various propellant combinations – includes mixing, burn rates, etc. (table 5.6 in Humble).

where Dt is the throat diameter in centimeters. Relation plotted for 1/5 < Ac/At < 13.5and 0.7cm < Dt < 200cm

EXTROVERT Space Propulsion 05Ranges of Combustor Characteristic Length

Propellants Characteristic Length L*Low(m) High(m)

Liquid fluorine / hydrazine 0.61 0.71Liquid fluorine / gaseous H2 0.56 0.66

Liquid fluorine / liquid H2 0.64 0.76

Nitric acid/hydrazine 0.76 0.89N2O4 / hydrazine 0.60 0.89

Liquid O2/ ammonia 0.76 1.02

Liquid O2 / gaseous H2 0.56 0.71

Liquid O2 / liquid H2 0.76 1.02

Liquid O2 / RP-1 1.02 1.27

H2O2 / RP-1 (incl. catalyst) 1.52 1.78

EXTROVERT Space Propulsion 05Contraction Ratio vs. Throat diameter

Also, the contraction rate can be empirically determined as a function of Dt.

Chang gives a range from 2 to 5 for the ec for low thrust engines (smaller Dt), and from 1.3 to 2.5 for higher thrust engines (Larger Dt). Knowing L* and ec for a given At and propellant, we can estimate the required combustor length, Lc, for the cylinder section.

EXTROVERT Space Propulsion 05Sources of losses

1. We have already discussed the effect of non-axial flow at the nozzle exit.

Other sources of losses

2. Friction: Small in large engines, but can be significant for large e.

3. Heat loss

- Exit velocity is lower than expected due to enthalpy losses (fairly small).

Non-uniform flow at exit

- can be a big effect if the nozzle flow is separated inside.

- Open cycle mass flow losses

Note that the mas flow rate through the throat, which is what goes through the nozzle, may be less than the propellant consumption rate, because some of the propellant is diverted to run the pumps or not recaptured after use as coolant.

EXTROVERT Space Propulsion 05Losses (continued)

4. Nozzle chemistry (recombination) Recombination can actually increase C* above the frozen flow nozzle assumption as species recombine

if equilibrium flow is assumed.

if frozen flow is assumed

and

Taken together, all of these corrections will yield a “real” lambda of 0.9 to 0.98 (Humble pp.206) depending on the cycle, nozzle, throat losses, etc.

ae6450 fall 2008 lecture #5 nozzles

Documents

nozzle performance

rocket nozzle

nozzle characteristics

burnoutplug nozzle

nozzle problems

nozzle size

divergent nozzle

nozzle throat area